Tower of Function Fields by García and Stichtenoth

Let b = q2 be the square of a prime power q. In [1] García and Stichtenoth consider the tower F1 ⊆ F2 ⊆ ⋯ of global function fields over Fb, where F1 is the rational function fieldFb(x1) and Fi+1 := Fi(zi+1) for i = 1, 2,…, where zi+1 satisfies the equation